Question

prove that n2 - n is divisible by 2 for every positive integer n.

Answer 1

Step-by-step explanation:

(3^2-3)/2

=6/2

=3

it's an example

Answer 2

Case i: Let n be an even positive integer.

When n = 2q

In this case , we have

n² − n = (2q)² − 2q = 4q² − 2q = 2q (2q − 1)

n² − n = 2r , where r = q (2q − 1)

n² − n is divisible by 2 .

Case ii: Let n be an odd positive integer.

When n = 2q + 1

In this case,

n² − n = (2q + 1)² − (2q + 1) = (2q + 1) [ 2q + 1 − 1 ] = 2q (2q + 1)  

# Here (2q + 1) was taken common .

n² − n = 2r, where r = q (2q + 1)

n² − n is divisible by 2.

∴  n² − n is divisible by 2 for every integer n.